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Byju's Answer
Standard XII
Mathematics
Continuity of a Function
Discuss the c...
Question
Discuss the continuity of
f
(
x
)
=
sin
|
x
|
.
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Solution
Given,
f
(
x
)
=
sin
|
x
|
Let
a
be any real number.
Now, LHL at
x
=
a
,
lim
x
→
a
−
f
(
x
)
=
lim
h
→
0
f
(
a
−
h
)
=
lim
h
→
0
sin
|
a
−
h
|
=
sin
|
a
|
RHL at
x
=
a
,
lim
x
→
a
+
f
(
x
)
=
lim
h
→
0
f
(
a
+
h
)
=
lim
h
→
0
sin
|
a
+
h
|
=
sin
|
a
|
Also,
f
(
a
)
=
sin
|
a
|
⇒
lim
x
→
a
−
f
(
x
)
=
lim
x
→
a
+
f
(
x
)
=
f
(
a
)
Thus
f
(
x
)
is continuous at
x
=
a
.
Since
a
is an arbitrary real number, hence
f
(
x
)
is continuous everywhere.
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